Sums of the choose function and the Binomial Formula

Here’s a little maths thing. I was thinking about this game called Kniffel, which is a German game played with 5 dice. The internet says it has similar rules to Yahtzee though both seem to have many variants. The aspect that is important here is that you roll your 5 dice and then you may choose to re-roll any subset of them (up to twice). You choose which subset to re-roll in order to maximise your chances of achieving certain goals, like getting 5 o...